Looks like a bug in the library. If you use a tmp variable it works fine.
var bigInt = require('big-integer');
var number = bigInt(1);
var last = bigInt(1);
for(i=0;i<50;i++){
//number = number.add(last);
//last = number.minus(last);
var tmp = number.add(last);
last = number;
number = tmp;
console.log((i + 3) + ":" + number.toString());
}